On Defining Ex Ante Payoffs in Games with Diffuse Prior

Indiana University - Kelley School of Business - Department of Business Economics & Public Policy

Date Written: May 2, 2017

Abstract

We formalize the notion of a diffuse prior and show that, for a general class of games, strategies which admit well-defined expected payoffs under the diffuse prior satisfy a stationarity property. We define the diffuse prior through a limit construction, using sequences of well-defined priors that become increasingly dispersed and uniform. Admissible strategies are those for which ex ante payoffs along these sequences converge to a limit that does not depend on the particular sequence of priors. We show that a strategy is admissible if and only if it is almost stationary in a precise sense. A secondary contribution of the paper is a generalization of the concept of distributional strategies (Milgrom and Weber, 1985) to multistage games.